Melt the butter in a large pot over medium heat. Add the onion and garlic and sauté until the onion is translucent, about 5 minutes.

Add the broccoli and broth to the pot and bring to a boil. Reduce the heat to a simmer and let the soup cook for about 10 minutes, or until the broccoli is tender.

Using an immersion blender or a blender, puree the soup until smooth.

Stir in the heavy cream and cheddar cheese until the cheese is melted.

Season with salt and pepper to taste.

Serve the soup hot, garnished with additional cheddar cheese if desired.